Rewrite as a simplified fraction. ${1.1\overline{73} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1173.7373...\\ 10x &= 11.7373...\end{align*}}$ Subtracting the two equations, we have: ${990x = 1162}$ ${x = \dfrac{1162}{990}} $ ${x = \dfrac{581}{495}} \text{or} {1 \dfrac{86}{495}}$